Finite Group Databasebeta

← #14646271

Subgroups — #14646271

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068544C211yesmaximal, characteristic, complemented
2#13068534C211yesmaximal, characteristic, complemented
3#13067149C212yesmaximal, complemented
4#13067145C212yesmaximal, complemented
5C2×C11×#537C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic, complemented
7C22×C11×#41C2211yescharacteristic
8C11×#537—24no—
9C11×#537—24no—
10C2×C11×C22⋊Q8—21no—
11C2×C11×C22⋊Q8C411yescharacteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#121—21no—
14C2×C11×#121—21no—
15C2×C11×#121—21no—
16C2×C11×#121C411yescharacteristic, complemented
17C2×C11×#121C2211yescharacteristic
18C22×C11×C4⋊C4C411yescharacteristic, complemented
19C2×#66900—21no—
20C2×#66898—21no—
21C2×#66898—21no—
22C2×#66897—21no—
23#10622824C2212yes—
24#10622820C2212yes—
25#10622176—24no—
26#10622175—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—42no—
32C2×C11×#41—42no—
33C2×C11×#41—42no—
34C2×C11×#41—42no—
35C22×Q8×C11C2×C411yescharacteristic
36C22×Q8×C11D411yescharacteristic
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11D411yescharacteristic
42C22×D4×C11D411yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8D414yes—
54C11×#121—28no—
55C11×#121—28no—
56C11×#121—28no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121D414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—22no—
73C2×#4318—22no—
74#66900—42no—
75#66898—42no—
76#66898—42no—
77#66897—42no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)—22no—
82#8517—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11C22⋊C411yescharacteristic
85C24×C11C22⋊C411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C11×#41—48no—
88C11×#41—48no—
89C11×#41—48no—
90C11×#41—48no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11C22⋊C412yes—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—82no—
116C2×D4×C11—82no—
117C2×D4×C11C22⋊C412yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—82no—
136C22×C4×C11C22⋊C411yescharacteristic
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×Dic11—42no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4C22⋊C412yes—
149C11×C4⋊C4C22⋊C412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C22⋊Dic11—42no—
155C22⋊Dic11—42no—
156#4318—42no—
157#4318—42no—
158C2×C11⋊C8—42no—
159C2×#537D1111yescharacteristic
160#1785—111no—
161#1782—111no—
162#1511—112no—
163#1510—112no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—22no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11#9912yes—
183C23×C11C2×C22⋊C411yescharacteristic
184C23×C11#12012yes—
185Q8×C11—44no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—44no—
189D4×C11—44no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—44no—
193D4×C11—48no—
194D4×C11—84no—
195D4×C11—84no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—84no—
220C2×C4×C11#9912yes—
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11#12012yes—
224C2×Dic11—82no—
225C2×Dic11—82no—
226C2×Dic11—82no—
227C11⋊C8—82no—
228C22×#41Dic1111yescharacteristic, complemented
229C22×#41C2×D1111yescharacteristic
230#537—24no—
231#537—24no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8Dic1111yescharacteristic, complemented
234C2×C22⋊Q8C2×D1111yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121Dic1111yescharacteristic, complemented
239C2×#121C2×D1111yescharacteristic
240C22×C4⋊C4Dic1111yescharacteristic, complemented
241C2×#101—221no—
242C2×#100—221no—
243C2×#99—221no—
244C2×#99—221no—
245#407—112no—
246#381—112no—
247#328—224no—
248#327—224no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—42no—
261C22×C11—41no—
262C22×C11—42no—
263C22×C11—41no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11#37911yescharacteristic
272C22×C11C2×#9911yescharacteristic
273C22×C11C2×#9911yescharacteristic
274C4×C11—22no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—41no—
281C4×C11—42no—
282Dic11—162no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—42no—
288C2×#41—42no—
289C2×#41—42no—
290C2×#41—42no—
291C22×Q8C2×Dic1111yescharacteristic
292C22×Q8C22⋊D1111yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C2×Dic1111yescharacteristic
297C22×D4C22⋊D1111yescharacteristic
298C22×D4C22⋊D1111yescharacteristic
299C22×D4C22⋊D1111yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4C2×Dic1111yescharacteristic
303C23×C4C2×Dic1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×M16—222no—
306C22⋊Q8—28no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8C22⋊D1114yes—
311#121—28no—
312#121—28no—
313#121—28no—
314#121—22no—
315#121—22no—
316#121—22no—
317#121C22⋊D1114yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4C2×Dic1111yescharacteristic
324C2×C4⋊C4C2×Dic1111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—222no—
330#101—442no—
331#100—442no—
332#99—442no—
333#99—442no—
334C22⋊C8—222no—
335C22⋊C8—222no—
336#95—222no—
337#95—222no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—42no—
341C2×C11—42no—
342C2×C11—81no—
343C2×C11—82no—
344C2×C11#178111yescharacteristic
345C2×C11#179511yescharacteristic
346C2×C11#179611yescharacteristic
347C24—21no—
348C24C22⋊Dic1111yescharacteristic
349C24C22⋊Dic1111yescharacteristic
350C24C2×C22⋊D1111yescharacteristic
351#41—48no—
352#41—48no—
353#41—48no—
354#41—48no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8C22⋊Dic1112yes—
362C2×D4—24no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—24no—
368C2×D4—24no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—82no—
380C2×D4—82no—
381C2×D4C22⋊Dic1112yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—82no—
400C22×C4—442no—
401C22×C4C22⋊Dic1111yescharacteristic
402C22×C4C22⋊Dic1111yescharacteristic
403C22×C4C22×Dic1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1112yes—
407M16—442no—
408M16—442no—
409C2×C8—442no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—24no—
415C4⋊C4C22⋊Dic1112yes—
416C4⋊C4C22⋊Dic1112yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—442no—
422C22⋊C4—442no—
423C11#851711yescharacteristic, complemented, Sylow
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23#6689812yes—
443C23C2×C22⋊Dic1111yescharacteristic
444C23#6700612yes—
445Q8—44no—
446Q8—42no—
447Q8—42no—
448D4—44no—
449D4—44no—
450D4—42no—
451D4—42no—
452D4—44no—
453D4—48no—
454D4—84no—
455D4—84no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—84no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4—882no—
483C2×C4#6689812yes—
484C2×C4C2×C22⋊Dic1111yescharacteristic
485C2×C4C2×C22⋊Dic1111yescharacteristic
486C2×C4#6700612yes—
487C8—882no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—82no—
509C22—82no—
510C22C2×#6689811yescharacteristic
511C22C2×#6689811yescharacteristic
512C22#1062286011yescharacteristic
513C4—22no—
514C4—22no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—1762no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—42no—
526C2—82no—
527C2—81no—
528C2#1306853111yescharacteristic
529C2#1306858611yescharacteristic
530C2#1306859111yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#537C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC2×#537D11
hypocenterC11#8517
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13068544C2semidirect
2. #13068534C2semidirect
3. #13067149C2semidirect
4. #13067145C2semidirect
6. C22×C11×#41C4semidirect
11. C2×C11×C22⋊Q8C4semidirect
16. C2×C11×#121C4semidirect
18. C22×C11×C4⋊C4C4semidirect
228. C22×#41Dic11semidirect
233. C2×C22⋊Q8Dic11semidirect
238. C2×#121Dic11semidirect
240. C22×C4⋊C4Dic11semidirect
423. C11#8517semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130685442
#130685342
#130671492
#130671452
C2×C11×#5372
#851711